Editing Talk:1516: Win by Induction
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The explanation currently says that doubling makes it uncountably infinite. I'm pretty sure that doubling at each step (or every few steps) is still a countable infinite set. Proof here: http://practicaltypography.com/the-infinite-pixel-screen.html (see section "The internet demands a recount", because the first attempt is wrong). We can also prove it using the same argument as when proving that N x N is countable infinite (making zig-zag), but in this case making a breadth-first search of the tree of Pikachus: map 1 to the first Pikachu, map 2 and 3 to the two Pikachus at the second level, map 4, 5, 6, 7 to the four Pikachus at the third level, map (2^(n-1))…((2^n) - 1) to the 2^(n-1) Pikachus at level n. {{unsigned ip|108.162.229.177}} | The explanation currently says that doubling makes it uncountably infinite. I'm pretty sure that doubling at each step (or every few steps) is still a countable infinite set. Proof here: http://practicaltypography.com/the-infinite-pixel-screen.html (see section "The internet demands a recount", because the first attempt is wrong). We can also prove it using the same argument as when proving that N x N is countable infinite (making zig-zag), but in this case making a breadth-first search of the tree of Pikachus: map 1 to the first Pikachu, map 2 and 3 to the two Pikachus at the second level, map 4, 5, 6, 7 to the four Pikachus at the third level, map (2^(n-1))…((2^n) - 1) to the 2^(n-1) Pikachus at level n. {{unsigned ip|108.162.229.177}} | ||
:Saw this too late. Yes, I agree, and I have fixed it accordingly. --[[User:Stephan Schulz|Stephan Schulz]] ([[User talk:Stephan Schulz|talk]]) 09:28, 24 April 2015 (UTC) | :Saw this too late. Yes, I agree, and I have fixed it accordingly. --[[User:Stephan Schulz|Stephan Schulz]] ([[User talk:Stephan Schulz|talk]]) 09:28, 24 April 2015 (UTC) | ||
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"infinite, but countable" {Cough.} Someone doesn't understand infinity. Perhaps they meant "enumerable". [[Special:Contributions/108.162.250.155|108.162.250.155]] 09:29, 24 April 2015 (UTC)ū | "infinite, but countable" {Cough.} Someone doesn't understand infinity. Perhaps they meant "enumerable". [[Special:Contributions/108.162.250.155|108.162.250.155]] 09:29, 24 April 2015 (UTC)ū |